Using GRTensorII in the canonical
formalism of General Relativity
by
Dumitru N. Vulcanov
Department of Theoretical and Computational Physics
The West University of Timisoara, Timisoara, RO-1900, Romania
vulcan@physics.uvt.ro

This example outlines an aplication of the Maple + GrTensorII enviroment for the canonical treatment of the general relativity (ADM formalism) based on the 3+1 split of spacetime. There are two version of the program below . The first one is devoted to the "pure" ADM formalism, using the notations and conventions as they are described in "Gravitation" by Wheeler, Misner Thorne (Freeman, 1973) in chapter 21, pg. 484 (canonical.mws and biaI_din.mpl). The program is adapted to the Bianchi I space time but can be easily modified for other examples. It produces the constraints equations (the hamiltonian one and the momentum constraitns) and the dymanical equations for the three dimensional metric and for the three dimensional momenta components. A version of the ADM reductional formalism is developed - this part is strongly depending on the symmetry of the space-time. The second worksheet (Desitter.mws and desitter_sf.mpl) is a modified form  of the first one to the ADM formalism widely used in numerical relativity. Here instead of the momenta canonical conjugated to the three dimensional metric we used the components of the extrinsic curvature. We included also the minimal interaction of a scalar field with gravitation. Both programs can be used in various topics from gravity theory, as hamiltonian or inflationary cosmology, and of course in generating initial data for numerical relativity.

  Last update: October 2000